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Download Mathematics Assignment for grade 11th and more Exercises Mathematics in PDF only on Docsity!
MATHEMATICS ASSIGNMENT CLASS XI This assignment includes high-order thinking questions, NCERT exemplar-inspired problems. Chapter: Sets Questions 1. LetA={xEN|x <20 and divisible by 3}, B = {x € N | x < 20 and divisible by 4}. Find Au B, AM B, A-B. Represent these sets using a Venn diagram. Prove or disprove: IfAc BandBcC, thenAcC. Let P be the set of prime numbers and let S = {t | 2t— 1 is a prime}. Prove that S c P. If A and B are two sets such that n(A) = 15, n(B) = 20 and n(A U B) = 30, find n(A N B). Prove that (AM B) uU (AN B') =A. From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the on Pen student has passed in at least one of the subject, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 Mathematics and Chemistry and at most 20 Physics and Chemistry. What is the largest possible number that could have passed all three examination? 7. For sets A=({1, 2,3, 4} and B = (3, 4, 5, 6}, verify (A - B) u (B- A) =(Au B) - (ANB). 8. Define the power set of A = {a, b, c} and state how many subsets it has. 9. Let A= {x € Z| x? < 9}. Write A in roster form and find its complement in U={xeZ|-5sxs5}. 10. Show that: n(A U B UC) = n(A) + n(B) + n(C) - n(AN B)- n(BN C)-n(C NA) + n(AN BNC) 11. For all sets A, Band C Is (A— B) N (C— B) = (AN C) — B? Justify your answer. Chapter: Complex Numbers 1. Solve the equation: x? + 1 = 0 in the set of complex numbers. 2. Simplify: (3 + 4i)(2 - 5i) and express the result in a + bi form. 3. If z= 3 - 4i, find |z| and Arg(z). 4. If the imaginary part of 21ziz+1+32,--132i2.+32. is —2, then show thatthe locus of the point representing z in the argand plane is a straight lined. Solve for x and y if (x + iy)? = 7 + 24). 6. If z= + ib satisfies z + 1/z = 2cos@, show that |z| = 1. 7. Find the value of P such that the difference of the roots of the equation x? —- Px + 8 = Ois 2. C Scanned with OKEN Scanner 8. Find the cube roots of unity and verify their properties geometrically. 9. If z = cos@ + i sin®, prove that z" = cos(n@) + i sin(n@) (De Moivre’s Theorem for integer n). 10. Find the modulus and argument of the complex number (3 - 4i)/(1 + 2i) 11. If a = cos @ + i sin, find the value of =. C Scanned with OKEN Scanner 
